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To be fair, not all plants are plant type pokemon, just like not all rocks are rock type pokemon. So vegetarians should be able to eat non-pokemon just fine.

But yeah, I don’t think any non-pokemon animals exist in the pokemon setting, so burgers are definitely pokemon.

Ryu

Non-Pokemon are seen from time-to-time. Also, the Pokedex constantly refers to Pokemon that resemble animals as ‘snake Pokemon’ or ‘rat Pokemon’. This has some implications about the existence of non-Poke animals.

Drscoobie

In the anime, there are normal fish and birds.
In other words, not all creatures are Pokemon.